Math CentralQuandaries & Queries


Question from Ashley, a student:

what is the variance of these scores 53,67,43,54,58,54,47,35,45,56,45,47,54


The variance measures how far the scores deviate from the mean. First calculate the mean of the scores. I'm going to call it M. Now one at a time subtract the mean from each score, that is calculate score - M for each score. Some of these will be positive and some negative, in fact if you add them you will see that the sum is zero. Now square each of these differences, that is for each score you now have (score - M)2. Total these numbers, I'm going to call the total SS for "sum of squares".

Let n be the number of scores you have, for this example n = 13. Depending on the situation and exactly what you are doing the variance is one of




For your situation I think the expression you want for the variance is SS/(n - 1).


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